A number to the 11th power divided by the same number to the 8th power equals 216. what is the number?

Answers

Answer 1
Let "a number" be signified by x.
"A number" to the 11th power,
x^11

divided by "the same number" to the 8th power,
x^11 / x^8

equals 216,
x^11 / x^8 = 216

Apply your exponent rule, division to subtraction,
x^(11-8) = 216
x^3 = 216

"the number" is being raised to the third power.
To isolate our number, x, we'll apply the inverse of raising to a power:
Taking a third root (or applying a 1/3 power).

[tex]\large\rm x = \sqrt[3]{216}[/tex]

and simplify,

x= 6
Answer 2

The number will be 6.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The algebraic expression is,

''A number to the 11th power divided by the same number to the 8th power equals 216.''

Now,

Let a number = x

So, we can formulate;

⇒ x¹¹ / x⁸ = 216

⇒ x ¹¹ ⁻ ⁸ = 216

⇒ x³ = 216

Take cube root both side, we get;

⇒ x = ∛216

⇒ x = 6

Thus, The number will be 6.

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Related Questions


High School Mathematics 5+3 pts


Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 each month.

Answers

what is the question?

How many ones are there in the number ab98 in base 16?

Answers

........................................................

A snail travels 3/8 feet in 1/2 hour. How many feet did the snail travel in one hour.

Answers

The answer to the question is 6/8 hours is how long the snail took
3/4th a foot in an hour.

if √a/√b=x, which statement must be true? A. x^2=a/b B. √x=a/b C. |x|=a/b D. x=a/b

Answers

Answer:

x^2 = a/b

Step-by-step explanation:

[tex]\frac{\sqrt{a}}{\sqrt{b} } =x[/tex]

If we have square root at the top and bottom then we take single square root with fraction inside

[tex]\sqrt{\frac{a}{b}} =x[/tex]

To remove square root we take square on both sides because square and square root will get cancelled

[tex]\frac{a}{b}=x^2[/tex]

x^2 = a/b is true

The statement that must be true is:

[tex]x^2 = a/b[/tex]

How to find an equivalent expression?

To find an equivalent expression, we just need to rewrite the given expression.

Here we will use the fact that the square root is distributive with respect to the division, which means that we can rewrite:

[tex]\frac{\sqrt{a} }{\sqrt{b} } = x\\\\\sqrt{\frac{a}{b} } = x[/tex]

Now if we square both sides of that expression, we will get:

[tex]\sqrt{\frac{a}{b} }^2 = x^2\\\\\frac{a}{b} = x^2[/tex]

So we can see that the correct option is A.

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Which statements are true? Choose all answers that are correct. A. All quadrilaterals can be classified as either parallelograms or trapezoids. B. All rhombuses are parallelograms. C. Some trapezoids are parallelograms. D. Some parallelograms are squares.

Answers

Statements 'A', 'B', and 'C' are true.

Answer:

A, B and C

Step-by-step explanation:

An experienced bricklayer can construct a small wall in 4 hours. an apprentice can complete the job in 12 hours. find how long it takes if they work together.

Answers

Experienced worker takes 4hr to complete so in 1hr it would be 1/4 completed.
Apprentice worker takes 12hrs to complete, so in 1hr it would be 1/12 completed.
Team effort X hours and 1/X part of the job completed in an hour.

Set up:

1/4 + 1/12 = 1/x
Get the denominators the same to add. So multiply the left side by 3.
3/12 + 1/12 =1/x
Combine like terms.
4/12 = 1/x
Cross multiply.
4x = 12
Dived by 4 on both sides
X = 3 hrs if they work together.

The answer is 3.

They take 3 hours to complete the work together.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

An experienced bricklayer can construct a small wall in 4 hours.

And, An apprentice can complete the job in 12 hours.

Now,

Since, An experienced bricklayer can construct a small wall in 4 hours.

Hence, In 1 hour it will be completed 1/4 work.

And, An apprentice can complete the job in 12 hours.

So, In 1 hour it will be completed 1/12 work.

Let number of hour to complete the work together = x

in 1 hour both together completed 1/x work.

So, we can formulate;

1/4 + 1/12 = 1/x

Solve for x;

3/12 + 1/12 = 1/x

4/12 = 1/x

1/3 = 1/x

x = 3 hours.

Thus, They take 3 hours to complete the work together.

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MATH HELP!!!!!!!!!!!!!!!!!!!!!!!!1

Answers

4(50) +3r = 365

200+3r = 365

3r =165

r = 165/3

r = 55

A 2.2 GB game is being downloaded on your laptop. When you have downloaded half a gigabyte, you notice that your computer has been downloading at the rate of .01GB per minute. (A) Write an inequality that represents at least how many minutes it will take to download the game (b) Your computed only has two hours of battery life, will it be enough to download the game?

Answers

Final answer:

The game which is 2.2 GB will need 170 minutes to download at a rate of 0.01 GB per minute. But the computer has only 120 minutes of battery life which is insufficient.

Explanation:

The total size of the game is 2.2 GB. The part that is already downloaded is 0.5 GB, so the remaining size of the game to be downloaded is 2.2 GB - 0.5 GB = 1.7 GB. Now, since the downloading speed is 0.01 GB/minute, we extrapolate the remaining time as (1.7 GB) / (0.01 GB/min) which equals 170 minutes.

(a) So, the inequality representing at least how many minutes it will take to download the rest of the game is x ≥ 170, where x is the required time in minutes.

(b) Two hours of battery life is equivalent to 2*60 = 120 minutes. Since 170 minutes is required to download the game and the available battery life is only 120 minutes, the battery will not be enough to download the game.

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Jason draws a line in the sand at the beach. The line is 78 ft long. He wants to divide the line into sections that are each 1/8 ft long.

How many sections will the line be divided into?

Enter your answer in the box.

Answers

Basically you multiply 78x8 which equals 624 sections.

What is (are) the x-intercepts of the function graphed above?

Answers

The answer is (0,-4)

Answer:

The x intercepts are -4, -1 and 5 or (-4,0), (-1,0) and (5,0).

Step-by-step explanation:

Consider the provided graph.

Here we need to find the x intercepts of the function.

The x-intercepts are where the graph crosses the x-axis.

Here, the  provided graph crosses the x axis 3 times.

Thus there must be 3 x intercepts of the function.

Now label the points on which graph intersect the x axis as shown in figure 1.

Thus the labeled points are (-4,0), (-1,0) and (5,0)

Hence, the x intercepts are (-4,0), (-1,0) and (5,0) or -4, -1 and 5.

Calculate the theoretical probability that sum of 2 rolls equals 7

Answers

P(3 then a 4) =  1/6 * 1/3 = 1/36
P(4 then a 3) = 1/36

Theoretical probability = 1/36 + 1/36  = 1/18

A sculpture is shaped like a sphere with 4 cones attached to it. Several dimensions of the sculpture, in feet, are shown in the diagram below. The total height of the sculpture from top to bottom is 12 feet. What is the volume of the sculpture, to the nearest cubic foot? 

Answers

volume of the center sphere = 4/3*PI*r^3

r = 3 ( given in the picture)

 so 4/3 * 3.14 *3^3 = 113.04 cubic feet

 volume of 1 cone: pi *r^2 *h/3

r = 3 and h=3 ( given in the picture)

so 3.14 * 3^2 * 3/3 = 28.26 cubic feet

 there are 4 cones so 28.26* 4 = 113.04 cubic feet


113.04 + 113.04 = 226.08 cubic feet

 rounded to nearest cubic foot = 226 cubic feet

A parchment fragment was discovered that had about 61% as much 14c radioactivity as does plant material on earth today. estimate the age of the parchment. (round your answer to the nearest hundred years.)

Answers

The estimated age of the parchment is approximately 4,086.17 years.

To estimate the age of the parchment, we can use the concept of carbon dating.

Carbon-14 (14C) is a radioactive isotope of carbon that is commonly used for dating archaeological artifacts.

The amount of 14C in an organism remains relatively constant while the organism is alive because it continuously takes in carbon from the atmosphere and food.

However, after the organism dies, it no longer takes in new carbon, and the 14C begins to decay at a known rate.

The half-life of carbon-14 is approximately 5,730 years. This means that after 5,730 years, half of the original amount of carbon-14 in a sample would have decayed.

Let's use the information provided: the parchment fragment had about 61% as much 14C radioactivity as does plant material on Earth today.

This means that the remaining 14C in the parchment is 61% of the original amount. The remaining 14C is the amount that has not yet decayed, and the rest has decayed over time.

Now, we can set up an equation:

[tex]0.61 = (1/2)^{(t/5730)[/tex]

Where:

t = time in years since the parchment was alive.

Now, we need to solve for 't.' Taking the logarithm of both sides to isolate 't':

[tex]\log(0.61) = (t/5730) \times \log(1/2)[/tex]

Now, solving for 't':

[tex]t = (5730 \times \log(0.61)) / \log(1/2)[/tex]

Using a calculator, we find:

t ≈ 4,086.17 years

So, the estimated age of the parchment is approximately 4,086.17 years.

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Final answer:

Using the concept of radiocarbon dating and the fact that the parchment has 61% as much 14C radioactivity as present plant material, the calculated estimate for the parchment's age is approximately 2,200 years, rounded to the nearest hundred years.

Explanation:

To estimate the age of the parchment based on the information that it had about 61% as much 14C radioactivity as does plant material on Earth today, we use the concept of radiocarbon dating. The half-life of carbon-14 (14C) is 5,730 years, which means after every 5,730 years, the amount of 14C decreases by half. Given that the parchment retains 61% of its original 14C, we can formulate the decay equation to solve for the parchment's age.

The decay equation is given by: \(N_t = N_0(1/2)^{t/T}\), where \(N_t\) is the remaining amount of 14C, \(N_0\) is the original amount of 14C, \(t\) is time, and \(T\) is the half-life of 14C. In this case, \(N_t/N_0 = 0.61\), and we know \(T = 5730\) years.

By substituting the given values into the decay equation and solving for \(t\), we find that the parchment is approximately 2,200 years old, rounded to the nearest hundred years. This estimation assumes the natural 14C to 12C ratio in the atmosphere has been constant over the time period in question.

Cheryl wants to purchase a par value $500 bond from Agram Imports. Agram imports bonds have a market rate of 102.114 and offer 8.1% interest. If Cheryl’s broker charges a commission of 2.5% of the market value of each bond sold, what is the current yield on Cheryl’s bond?

A. 0.077
B. 0.078
C. 0.081
D. 0.040

Answers

According to my study,  current yield is calculated by using the formula Interest or dividends divided by the current price of the security or simple the current price. So the current price in this given question is 102.114 and the interest is 8.1%, we will simply divide the two; 8.1 / 102.114 = 0.07732310947 or approximately .077. The answer is A.

Answer:

the answer is A. my friends

nx-r=p
We need to solve for x.

Answers

think of the = sign as a balance beam, every time you move a number across it the sign will change (ex: 1x+3=6-2 if u move the 3 across to have just the x variable you will have 1x=6-2-3 or 1x=6-5) so nx-r=p would be nx=p+r if u are solving for x you want to divide by the number attached to x which is n you do x/n=p+r/n. and since there are no numbers you cannot solve any further

A circle has a diameter of 12mm . what is its circumference? use 3.14 for π , and do not round your answer. be sure to include the correct unit in your answer.

Answers

c=πd therefore the answer is 37.68 mm

With a diameter of 12mm and using π as 3.14, the circumference is calculated as 37.68mm.

The circumference of a circle can be calculated using the formula:

Circumference = π x diameter

Given: Diameter = 12mm

Using π = 3.14:

Circumference = 3.14 x 12mm = 37.68mm

Therefore, the circumference of the circle is 37.68mm.

what is the perimeter of this triangle

Answers

18m^3 + 2m^2 -1m hope this helped

write the equation 10x+5y=5 in the slope intercept form. Then graph the line

Answers

Final answer:

The equation 10x+5y=5 can be rewritten in slope-intercept form as y = -2x + 1. This equation's slope is -2 and the y-intercept is 1. The line intercepts the y-axis at (0,1) and for every 1 unit increase in x, y decreases by 2 units.

Explanation:

To write the equation 10x+5y=5 in slope-intercept form, you need to solve for y. The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

First, divide the entire equation by 5 to simplify it:

(10x+5y)/5 = 5/5 becomes 2x + y = 1.

Then, solve the equation for y:

y = -2x + 1

The slope (m) of the equation is -2 and the y-intercept (b) is 1. Therefore, the line intercepts the y-axis at the point (0,1) and for every 1 unit increase in x, y decreases by 2 units due to the negative slope.

To graph this line, first plot the y-intercept at the point (0,1). Next, from this point, move right 1 unit (increase in x) and down 2 units (decrease in y) to get the point (1,-1). Draw a straight line through these points to represent the equation y = -2x + 1.

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A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. a marble is chosen at random from the jar. after replacing it, a second marble is chosen. what is the probability of choosing a green and then a yellow marble

Answers

Add the numbers up (leads to 16) and then make it a fraction so out the number of green over 16 leaving you with the fraction answer of 5/16

The Tigers lost 15% of the 60 games that they played this season. How many games did they win?

Answers

The first step, would be to make the percent a fraction. 15%=15/100.

So, if they played 60 games, and you want to find how many they lost, you would write x/60, when x=games lost.

15     x
___=___
100   60

Simplify the fraction on the left. Divide the numerator (top) and the denominator (bottom) by 5, leaving you with 3/20.

3/20=x/60

Make the denominators (bottom) similar

9/60=x/60

x=9
  

Write the number 7362 to the nearest thousand

Answers

7,000 is the answer, brainiest would be wonderful. :)
7000 because 2<5 to move up and 6>5 so the three becomes a 4 and 4<5 so now you’re stuck with 7000 if you understand what I mean.

What is the perimeter of a polygon with vertices at (−1, 3) , ​ (−1, 6) ​, (2, 10) , ​ (5, 6) ​​, and ​​ ​ (5, 3) ​?

Enter your answer in the box. Do not round any side lengths.​

Answers

first you need to find the distance between the points using the distance formula d=
[tex] \sqrt{(x2 - x1) { }^{2} + (y2 - y1) {}^{2} } [/tex]
and once you find the distance for each side you add them all together to get the perimeter.

(Remember, x is the first number in the brackets and y is the second)

Answer:

FOR ALL THOSE LAZY PPL, HERE'S THE ANSWER....



22 units.

Have a nice day mates.



Find the value of x so the rectangles have the same area

Answers

Area of rectangles = width * length.
So x*12 = 12x = area of first rectangle
So 16*(x-2) = 16x -32 = area of second rectangle

The question states to make them equal, so:
first rectangle = second rectangle
12x = 16x -32
Solve for x
-4x = -32
4x = 32
x = 8

 
The rectangular area to find the area that these objects occupy.  The area of the rectangle is the multiplication of the length and width.

Using formula:

Area of rectangles = width [tex]\bold{\times}[/tex] length.

Using the first image to calculate the area:

[tex]\to \bold{ x\times 12 = 12x }[/tex]

Using the second image to calculate the area:

[tex]\to \bold{16\times (x-2) = 16x -32 }[/tex]

equalling both the area:

[tex]\to \bold{12x = 16x -32}\\\\\to \bold{32 = 16x -12x}\\\\\to \bold{32 = 4x }\\\\\to \bold{4x=32 }\\\\\to \bold{x=\frac{32}{4}}\\\\\to \bold{x=8}\\\\[/tex]

Learn more:

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Evaluate the expression 15/3x-6, when x=4.

Answers

The answer is:  5/2 ; or, write as:  "½ " ; or, write as:  "2.5" .
___________________________________________________
15/ (3x - 6) ;

Substitute "4" for "x" ; and solve:
___________________________________________________

Note:  (3x -6) = 3(4) - 6 = 12 - 6 = 6 ; 

Rewrite the expression:

15/6 = (15 ÷ 3) / (6 ÷ 3) = 5/2 ; or, write as:  "½ " ; or, write as:  "2.5" .
___________________________________________________

The expression 15/3x-6 evaluates to -4.75 when x=4. The solution involves substitution followed by the order of operations: first multiplication, then division, and finally subtraction.

The student asked to evaluate the expression 15/3x-6 when x=4. To do this, we first substitute the value of x into the expression, which then becomes 15/(3*4)-6.

Now we simplify the expression step by step:

Multiply 3 by 4, which is 12.Divide 15 by 12, which gives 1.25.Subtract 6 from 1.25, which results in -4.75.

So, when x equals 4, the value of the expression 15/3x-6 is -4.75.

Which is the endpoint of a ray?

point R
point S
point T
point U

Answers

The answer is point S
Hope this helps 

The endpoint of a ray in the diagram given is the point S.

A ray is often referred to as the sides of a angle.

An angle is produced when two different rays share or have a common endpoint which forms the vertex.

From the diagram given above ; an angle is formed at S.

S depicts a point where three different rays meet.

Rays SR, SU and ST

SINCE , the point where two or more rays meet leading to the formation of an angle is called an endpoint. Then , point S is an endpoint.

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Kelly wants to know the actual value of a house that she wants to buy. What should she do?

Answers

Kelly should ask the realtor.

for plato the answer is, c. get a real-estate appraisal

posting this for future users!

How many different sums of money can be formed from penny and half a dollar?

Answers

so its a penny and a half dollar that will give you $0.51 so you can do this
starting with your 51 pennies you can get rid of every 5 pennies and replace them with a nickel so say you get rid of 10 pennies you would have 2 nickels
so 51/5= 10.2
or 10 nickels
so that is ten combos right there along side 51 pennies
so no you do the dimes witch for every 10 pennies you get rid of is = to 1 dime so 51/10=5.1 or 5 dimes so that gives you 5 more combos
so now its 1 penny combo with 10 nickel combos with 5 dime combos
now for quarters for every 25 pennies you get rid of is = to 1 quarter so
51/25=2.04 or just 2 and with half dollars ( they do make thoses ) it is for every 50 pennies you get rid of is = to one half dollar ( which is 50 cents) so 51/50= 1.02 or 1 so it is
1 penny combo + 10 nickels combos + 5 dime combos + 2 quarter combos + 1 half dollar combo =
1+10+5+2+1=19 different sums of money 

A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent?


A) Dependent because the women both received a pink rose.
B) Independent because the women both received a pink rose.
C) Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
D) Independent because when the first flower is taken, it does not change the ratio of the types of flowers in the vase.

Answers

It C because when u take away 2 it affects how many flowers are left

Answer:

Option C - Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

Step-by-step explanation:

Given : A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations.

One flower is chosen at random and given to a woman for her to keep.

Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose.

To find : Are these events independent or dependent?

Solution :

According to the statements,

The probability that the second woman receives a pink rose is dependent upon what the first woman receives.

Total flowers = 5+4+6=15

If the first woman does not receive a pink rose,

Then, the probability of the second woman receiving one is [tex]\frac{4}{15}[/tex]

If the first woman does receive a pink rose

Then, the probability of the second woman receiving one is  [tex]\frac{3}{15}=\frac{1}{5}[/tex]

Therefore, Option C is correct.

Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.

What is the value of the function at x=−2?



y=−2

y = 0

y = 2

y = 3


Answers

y=2
I hope I helped..

Answer:

y = 2

Step-by-step explanation:

When we have graph is given also one value from x and y is given then for finding the other value, We simply see the line where x = -2 is graphed and then we will see what is the value of y there.

Here at x = -2, y = 2 this is clearly apparent from the graph.

A candle is 7 in. tall after burning for 1 h. The same candle is in. tall after burning for 4 h. How tall will the candle be after burning for 6 h?

Answers

After burning 6 hours the candle will be 4 1/2 in. tall.

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